Value Distribution In P Adic Analysis

Author : Alain Escassut
Publisher : World Scientific
Page : 559 pages
File Size : 40,9 Mb
Release : 2015-11-27
Category : Mathematics
ISBN : 9789814730112

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Value Distribution in P-Adic Analysis by Alain Escassut Pdf

"The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard's problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard's values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida's equation."--

Author : Alain Escassut,Wolfgang Tutschke,C. C. Yang
Publisher : Unknown
Page : 631 pages
File Size : 51,9 Mb
Release : 2008
Category : Complex analysis
ISBN : 7030204069

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Some Topics on Value Distribution and Differentiability in Complex and P-adic Analysis by Alain Escassut,Wolfgang Tutschke,C. C. Yang Pdf

Author : Alain Escassut
Publisher : World Scientific
Page : 600 pages
File Size : 43,5 Mb
Release : 2015-11-27
Category : Mathematics
ISBN : 9789814730129

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Value Distribution in p-adic Analysis by Alain Escassut Pdf

' The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard''s problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard''s values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida''s equation. Contents: Ultrametric FieldsHensel LemmaSpherically Complete ExtensionsAnalytic ElementsPower and Laurent SeriesFactorization of Analytic ElementsDerivative of Analytic ElementsVanishing along a Monotonous FilterMaximum PrincipleQuasi-Invertible Analytic ElementsMeromorphic FunctionsThe Corona Problem on Ab(d(0,1‾))Applications to CurvesGrowth of the Derivative of an Entire FunctionRational Decomposition for Entire Functionsand other papers Readership: Graduate students and researchers interested in p-adic analysis. Keywords:p-Adic;Transcendental Numbers;Meromorphic;Nevalinna Theory'

Author : Alain Escassut
Publisher : World Scientific
Page : 349 pages
File Size : 49,5 Mb
Release : 2021-03-17
Category : Mathematics
ISBN : 9789811226236

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P-adic Analytic Functions by Alain Escassut Pdf

P-adic Analytic Functions describes the definition and properties of p-adic analytic and meromorphic functions in a complete algebraically closed ultrametric field.Various properties of p-adic exponential-polynomials are examined, such as the Hermite-Lindemann theorem in a p-adic field, with a new proof. The order and type of growth for analytic functions are studied, in the whole field and inside an open disk. P-adic meromorphic functions are studied, not only on the whole field but also in an open disk and on the complemental of an open disk, using Motzkin meromorphic products. Finally, the p-adic Nevanlinna theory is widely explained, with various applications. Small functions are introduced with results of uniqueness for meromorphic functions. The question of whether the ring of analytic functions—in the whole field or inside an open disk—is a Bezout ring is also examined.

Author : Khodr Shamseddine
Publisher : American Mathematical Soc.
Page : 305 pages
File Size : 53,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821891421

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Advances in Ultrametric Analysis by Khodr Shamseddine Pdf

This volume contains papers based on lectures given at the 12th International Conference on p-adic Functional Analysis, which was held at the University of Manitoba on July 2-6, 2012. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.

Author : Jr̲n Steuding
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 55,9 Mb
Release : 2007-06-06
Category : Mathematics
ISBN : 9783540265269

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Value-Distribution of L-Functions by Jr̲n Steuding Pdf

These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.

Author : Alain Escassut,Cristina Perez-Garcia,Khodr Shamseddine
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 55,7 Mb
Release : 2018-03-26
Category : Functional analysis
ISBN : 9781470434915

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Advances in Ultrametric Analysis by Alain Escassut,Cristina Perez-Garcia,Khodr Shamseddine Pdf

Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of -adic series, rational maps on the projective line over , non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, -modules with a convex base, non-compact Trace class operators and Schatten-class operators in -adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean Köthe spaces, -adic Nevanlinna theory and applications, and sub-coordinate representation of -adic functions. Moreover, a paper on the history of -adic analysis with a comparative summary of non-Archimedean fields is presented. Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 48,5 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401583565

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p-Adic Valued Distributions in Mathematical Physics by Andrei Y. Khrennikov Pdf

Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I· We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo· These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 163 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211129

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p-adic Numbers, p-adic Analysis, and Zeta-Functions by Neal Koblitz Pdf

The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gamma-function, the rearrangement and addition of some exercises, the inclusion of an extensive appendix of answers and hints to the exercises, as well as numerous clarifications.

Author : Fernando Q. Gouvêa
Publisher : Springer Nature
Page : 366 pages
File Size : 55,5 Mb
Release : 2020-06-19
Category : Mathematics
ISBN : 9783030472955

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p-adic Numbers by Fernando Q. Gouvêa Pdf

There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE

Author : Karl‐Olof Lindahl,Torsten Lindström,Luigi G. Rodino,Joachim Toft,Patrik Wahlberg
Publisher : Springer
Page : 568 pages
File Size : 42,8 Mb
Release : 2019-04-29
Category : Mathematics
ISBN : 9783030044596

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Analysis, Probability, Applications, and Computation by Karl‐Olof Lindahl,Torsten Lindström,Luigi G. Rodino,Joachim Toft,Patrik Wahlberg Pdf

This book is a collection of short papers from the 11th International ISAAC Congress 2017 in Växjö, Sweden. The papers, written by the best international experts, are devoted to recent results in mathematics with a focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on the current research in mathematical analysis and its various interdisciplinary applications.

Author : N. M. Chuong
Publisher : World Scientific
Page : 393 pages
File Size : 55,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770707

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Harmonic, Wavelet and P-Adic Analysis by N. M. Chuong Pdf

The mutual influence between mathematics and science and technology is becoming more and more widespread with profound connections among them being discovered. In particular, important connections between harmonic analysis, wavelet analysis and p-adic analysis have been found recently. This volume reports these findings and guides the reader towards the latest areas for further research. It is divided into two parts: harmonic, wavelet and p-adic analysis and p-adic and stochastic analysis.

Author : Jesus Araujo-Gomez,Bertin Diarra,Alain Escassut
Publisher : American Mathematical Soc.
Page : 294 pages
File Size : 51,8 Mb
Release : 2011
Category : Topological fields
ISBN : 9780821852910

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Advances in Non-Archimedean Analysis by Jesus Araujo-Gomez,Bertin Diarra,Alain Escassut Pdf

These collected articles feature recent developments in various areas of non-Archimedean analysis: Hilbert and Banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between Banach functions spaces, and measure and integration.

Author : Kiyoshi L Igusa,William Cherry,Chung-Chun Yang,Joint International Meeting of the American Mathematical Society and the Hong Kong Mathema
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 43,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829806

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Value Distribution Theory and Complex Dynamics by Kiyoshi L Igusa,William Cherry,Chung-Chun Yang,Joint International Meeting of the American Mathematical Society and the Hong Kong Mathema Pdf

This volume contains six detailed papers written by participants of the special session on value distribution theory and complex dynamics held in Hong Kong at the First Joint International Meeting of the AMS and the Hong Kong Mathematical Society in December 2000. It demonstrates the strong interconnections between the two fields and introduces recent progress of leading researchers from Asia. In the book, W. Bergweiler discusses proper analytic maps with one critical point and generalizes a previous result concerning Leau domains. W. Cherry and J. Wang discuss non-Archimedean analogs of Picard's theorems. P.-C. Hu and C.-C. Yang give a survey of results in non-Archimedean value distribution theory related to unique range sets, the $abc$-conjecture, and Shiffman's conjecture. L. Keen and J. Kotus explore the dynamics of the family of $f_\lambda(z)=\lambda\tan(z)$ and show that it has much in common with the dynamics of the familiar quadratic family $f_c(z)=z^2+c$. R. Oudkerk discusses the interesting phenomenon known as parabolic implosion and, in particular, shows the persistence of Fatou coordinates under perturbation. Finally, M. Taniguchi discusses deformation spaces of entire functions and their combinatorial structure of singularities of the functions. The book is intended for graduate students and research mathematicians interested in complex dynamics, function theory, and non-Archimedean function theory.

Author : Pei-Chu Hu,Chung-Chun Yang
Publisher : Springer Science & Business Media
Page : 546 pages
File Size : 48,8 Mb
Release : 2006-10-06
Category : Mathematics
ISBN : 9783764375690

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Value Distribution Theory Related to Number Theory by Pei-Chu Hu,Chung-Chun Yang Pdf

The subject of the book is Diophantine approximation and Nevanlinna theory. This book proves not just some new results and directions but challenging open problems in Diophantine approximation and Nevanlinna theory. The authors’ newest research activities on these subjects over the past eight years are collected here. Some of the significant findings are the proof of Green-Griffiths conjecture by using meromorphic connections and Jacobian sections, generalized abc-conjecture, and more.